Dynamics of certain anti-competitive systems of rational difference equations in the plane

Abstract

We consider two systems of rational difference equations in the plane:

and

where the parameters are positive numbers and initial conditions and are positive numbers. For the first system we obtain the global dynamics, whereas for the second system we obtain substantial global results for all values of parameters. Global dynamics of two systems is substantially different to the contrary of their similarities.

Keywords:

• competitive map
• global stable manifold
• monotonicity
• period-two solution

AMS 2000 Mathematics Subject Classification::

• Primary
• Secondary